Revealing asymmetric homoclinic and heteroclinic orbits

Jun Pan; Haijun Wang; Feiyu Hu; Jun Pan; Haijun Wang; Feiyu Hu

doi:10.3934/era.2025061

Electronic Research Archive

2025, Volume 33, Issue 3: 1337-1350. doi: 10.3934/era.2025061

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Research article

Revealing asymmetric homoclinic and heteroclinic orbits

Jun Pan ^{1
,
,},
Haijun Wang ^{2
,
,},
Feiyu Hu ³

1.
School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
2.
School of Electronic and Information Engineering (School of Big Data Science), Taizhou University, Taizhou 318000, China
3.
College of Sustainability and Tourism, Ritsumeikan Asia Pacific University, Beppu 874-8577, Japan

Received: 11 February 2025 Revised: 26 February 2025 Accepted: 28 February 2025 Published: 07 March 2025

Although scholars have proven the existence of a pair of homoclinic orbits to the origin, or a pair of heteroclinic orbits to the origin along with a pair of nontrivial equilibria in symmetric Lorenz, Chen, and Lü systems, they have rarely dealt with asymmetric ones of the corresponding asymmetric analogues, to the best of our knowledge. To clarify this subject, this work revisited an asymmetric Chen system and reveals a single/a pair of asymmetric heteroclinic/homoclinic orbits, which are justified with numerical experiments.
- asymmetric Chen system,
- a single/a pair of asymmetric heteroclinic/homoclinic orbits,
- Lyapunov function
Citation: Jun Pan, Haijun Wang, Feiyu Hu. Revealing asymmetric homoclinic and heteroclinic orbits[J]. Electronic Research Archive, 2025, 33(3): 1337-1350. doi: 10.3934/era.2025061

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Abstract

Although scholars have proven the existence of a pair of homoclinic orbits to the origin, or a pair of heteroclinic orbits to the origin along with a pair of nontrivial equilibria in symmetric Lorenz, Chen, and Lü systems, they have rarely dealt with asymmetric ones of the corresponding asymmetric analogues, to the best of our knowledge. To clarify this subject, this work revisited an asymmetric Chen system and reveals a single/a pair of asymmetric heteroclinic/homoclinic orbits, which are justified with numerical experiments.

References

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